1. Field of the Invention
The present invention relates to apparatus for measuring rotation. More particularly, this invention pertains to a phase modulator for use in a fiber optic Sagnac interferometer of the type that employs a closed-loop control system that relies upon a digital Serrodyne phase ramp.
2. Description of the Prior Art
The Sagnac interferometer is an instrument for determining rotation by measurement of the nonreciprocal phase difference generated between a pair of counterpropagating light beams. This instrument generally comprises a light source such as a laser, an optical waveguide consisting of several mirrors or a plurality of turns of optical fiber, a beamsplitter/combiner, a detector and a signal processor.
In an interferometer, the waves coming out of the beamsplitter counterpropagate along a single optical path. The optical waveguide is "reciprocal"; that is, any distortion of the optical path affects the counterpropagating beams similarly although they do not necessarily experience such perturbation at the same time or in the same direction. Time-varying perturbations may be observed where the time interval is comparable to the propagation time of the light around the optical waveguide whereas "nonreciprocal" perturbations affect the counterpropagating beams differently and according to the direction of propagation. Such nonreciprocal perturbations are occasioned by physical effects that disrupt the symmetry of the optical medium in which the two waves propagate.
Two of the nonreciprocal effects are quite well known. The Faraday, or collinear magneto-optic effect, occurs when a magnetic field creates a preferential spin orientation of the electrons in an optical material whereas the Sagnac, or inertial relativistic effect, occurs when rotation of the interferometer with respect to an inertial frame breaks the symmetry of propagation time. The latter effect is employed as the principle of operation of a ring gyroscope.
The measured or detected output of a gyroscope is a "combined" beam (i.e., a composite beam formed of the two counterpropagating beams after one complete traverse of the gyroscope loop.) The rotation rate about the sensitive axis is proportional to the phase shift that occurs between the counterpropagating beams. Accordingly, accurate phase shift measurement is essential.
FIG. 1 is a graph that illustrates the relationship between the intensity of the combined (output) beam and the phase difference between the counterpropagating composite beams. The fringe pattern as shown consists of two elements, a d.c. component and a component that is proportional to the cosine of the phase difference between the beams. Such phase difference provides a measure of the nonreciprocal perturbation due, for example, to rotation.
As a consequence of the shape of the fringe pattern, when small phase differences are to be measured (e.g. low rotation rates), the intensity of the combined beam is relatively insensitive to phase difference as the phase difference is then close to a maximum of the fringe pattern. Further, mere intensity of the composite beam does not indicate the sense or direction of rotation.
For the foregoing reasons, an artificially biased phase difference is commonly superimposed upon the counterpropagating beams. The biasing of the phase shift, also known as a "nonreciprocal null-shift", enhances the sensitivity of the intensity measurement to phase difference. A maximum degree of sensitivity is achieved by shifting the operating point of the gyroscope to .+-..pi./2. Furthermore, by alternating the bias between +.pi./2 and -.pi./2, two different operating points are observed. This enables the system to determine the sign of the phase difference and, thus, the direction of rotation.
In addition to phase modulation, the processing of the interferometer output commonly employs "phase-nulling" which introduces an additional phase shift through a negative feedback mechanism to compensate for that due to the non-reciprocal (Sagnac) effect. Commonly, the negative feedback generates a phase ramp whose slope is proportional to the rate of change of the measured phase difference. In actual practice, a ramp whose height varies between zero and 2.pi. radians is employed as the nulling phase shift cannot be increased indefinitely due to voltage constraints.
In the past, phase nulling has employed both analog and digital techniques. In analog phase nulling, a sawtooth waveform whose slope is proportional to the rate of change of the phase difference and whose peak-to-peak amplitude is equal to 2.pi. radians is combined with the above-described phase modulation (null shift) signal to drive the electro-optic phase modulator located within the gyroscope coil. The analog method is limited insofar as the scale factor of the phase modulation command differs from that utilized for the negative feedback. Furthermore, it is quite difficult to detect the 2.pi. radians peak-to-peak amplitude in the analog method described supra.
U.S. Pat. No. 4,705,399 of Graindorge, Ardity and Lefevre discloses a digitally-based arrangement that overcomes a number of the shortcomings of the analog sawtooth technique. In the patented system, a "stairstep" waveform replaces the sawtooth. The height of each step is equal to the measured phase difference while the width or duration of each is the group delay time of the optical coil. FIG. 2 is a graph of a portion of such a feedback ramp signal. On the average, the slope of the ramp is equivalent to the measured nonreciprocal phase difference per unit of time. Two waves whose respective delay is equal to the group delay of the gyro loop are always on two consecutive steps and their phases differ by .DELTA..phi..sub.0. This method is compatible with digital signal processing and enjoys many resulting advantages. Additionally, the phase modulation may be directly added to the digital ramp through the synchronization offered by a digital signal processor.
The (combined) signal ultimately controls the phase modulator that is positioned near one end of the optical fiber coil. This device may comprise an electrooptic crystal whose index of refraction is responsive to an applied voltage or a piezoelectric structure arranged to exert pressure upon the optical fiber in response to an applied voltage. The pressure, in turn, affects the refractive index of the somewhat-compressed optical fiber. In either case, the digital word that consists of the feedback (ramp)-plus-phase modulation information is converted to an analog signal prior to application to the phase modulator electrodes. This conversion requires both a digital-to-analog converter and a high speed operational amplifier, each of which is a relatively-expensive component.